The couple welcomed twins earlier this year via a surrogate, a source tells PEOPLE.
A rep for Wiig did not comment.
PEOPLE confirmed in August 2019 that the Bridesmaids star was engaged to Rothman.
In May, Wiig returned to Saturday Night Live as a host during the show’s Mother’s Day ‘At Home’ episode in which she hinted at becoming a mother by thanking her mom, Laurie Johnston, for “preparing me to be a mom myself.”
“This is the Mother’s Day show, and at SNL, it’s a very special time to celebrate moms,” Wiig said. “Unfortunately, probably like a lot of you, I can’t be with my mom on this Mother’s Day. So I hope it’s OK, I would like to tell her I love her.”
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Wiig continued, “I don’t know if I truly appreciated my mom the first 45 years of my life. But this year I’m feeling especially grateful for her advice, her love. I’m so thankful for all the things she’s taught me, like preparing to be a mom myself.”
She added, “Things like breastfeeding,” before lifting up a plate of cooked chicken breasts, saying, “Babies love that chicken, she would always say that.”
The couple was first spotted together in 2016, although they mostly keep their relationship out of the spotlight.
At the time, in 2016, the two were seen showing off some PDA in Kauai, Hawaii, and a source exclusively revealed to PEOPLE that the couple had been “dating for a few months.”
“They’re really happy together,” the source added.
Rothman is a writer, actor, producer and director who trained at the Groundlings theater in Los Angeles (where Wiig also studied). He directed the short film Bunion, which premiered at the WILDsound Film Festival in 2015.
“My sister got me in to yoga about seven years ago,” Rothman said. “For a while I became addicted and was in class five times a week.”
The Ghostbusters star was previously married to actor Hayes Hargrove in 2005 before the two divorced in 2009.